There is some evidence that the QSL in question is a chiral spin liquid, which would be compatible with a continuous transition to a chiral (\(d+id\) ) SC upon light doping, as shown in the figure. Then at larger doping and intermediate values of \(U/8t\) , there is evidence from DMRG studies of a local tendency toward a variety of possible broken symmetry phases including SDW, CDW, PDW and nematic SC. However, again, which of these orders exist as ground state phases in 2d is still an open question. Preliminary evidence [1]} that the SC tendencies are particularly strong at small \(x\)  and for \(U\)  in the spin-liquid regime offers some encouragement for the long cherished ideal that a spin liquid may be a high temperature superconductor waiting to happen.
